WASHINGTON (AP) – Senators from both parties started a fresh search Wednesday for compromise immigration legislation, but leaders conceded that the effort won't be easy and were already casting blame should the effort falter.

Around three dozen senators, evenly divided among Republicans and Democrats, planned to meet late Wednesday in what No. 2 Senate GOP leader John Cornyn of Texas said he hoped would "get people thinking about a framework that might actually work." Their goal is to produce a bipartisan package to protect from deportation the "Dreamers" – hundreds of thousands of immigrants in the U.S. illegally after being brought here as children – and to provide billions to toughen border security.

"We cannot let those who are anti-immigrant, who call giving the Dreamers hope 'amnesty,' block us. Because then we will fail, and it will be on the other side of the aisle that made that happen," said Senate Minority Leader Chuck Schumer, D-N.Y.

Schumer spoke about 12 hours after President Donald Trump put the onus on Schumer.

"Cryin' Chuck Schumer fully understands, especially after his humiliating defeat, that if there is no Wall, there is no DACA," the president tweeted late Tuesday, using the acronym for the Deferred Action for Childhood Arrivals program, which has allowed the roughly 700,000 immigrants to remain in the country. "We must have safety and security, together with a strong Military, for our great people!"

Schumer said Tuesday that he'd pulled back an offer of $25 billion for Trump's long-promised border wall with Mexico. An aide said Schumer had actually withdrawn the offer Sunday night after it became clear that there would be no quick compromise on protecting the Dreamers.

"So now the group has to start in a new way with no preconceptions, and come together and find a bill that can garner 60 votes," Schumer said, underscoring that Trump's rejection of an offer the Democrat made Friday on immigration and budget issues meant that the offer was no longer on the table.

Senate Minority Leader Mitch McConnell, R-Ky., has said if senators cannot produce a compromise plan by Feb. 8 – which both sides' leaders have said will be difficult – he will begin debating immigration legislation in a debate that will be "fair to all sides."